SOLUTION: I really need your help in solving this problem. I appreciate your time and efforts. Have a terrific day :) Here is the question: In a population of exam scores, a score of X=48

Algebra ->  Probability-and-statistics -> SOLUTION: I really need your help in solving this problem. I appreciate your time and efforts. Have a terrific day :) Here is the question: In a population of exam scores, a score of X=48      Log On


   

Question 1018967: I really need your help in solving this problem. I appreciate your time and efforts. Have a terrific day :) Here is the question:
In a population of exam scores, a score of X=48 corresponds to Z= +1.00 and a score of X = 36 corresponds to Z = - 0.50. Find the mean and standard deviation for the population.
Answer by mathmate(429) About Me  (Show Source):
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Question:
In a population of exam scores, a score of X=48 corresponds to Z= +1.00 and a score of X = 36 corresponds to Z = - 0.50. Find the mean and standard deviation for the population.

Solution:
Using Z=(X-μ)/σ,
we substitute into the given data:
1.0=(48-μ)/σ
=>
μ+σ=48........(1)
-0.50=(36-μ)/σ
=>
μ-0.5σ=36 .....(2)

(1)-(2)
1.5σ=12 =>σ=8.....(3)

Substitute (3) in (1)
μ+8=48 => μ=40 ......(4)

Check:
(48-40)/8=1
(36-40)/8=-0.5
so both are correct.